metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.36D14, Dic14.18D4, C4⋊C8⋊6D7, (C2×C4).39D28, C4.132(D4×D7), (C2×Dic28)⋊7C2, C28.341(C2×D4), (C2×C28).245D4, (C2×C8).131D14, C7⋊3(Q8.D4), (C4×Dic14)⋊17C2, C2.D56.2C2, C14.13(C4○D8), (C2×C56).24C22, (C4×C28).71C22, C4.D28.5C2, C28.330(C4○D4), C28.44D4⋊13C2, C2.13(C4⋊D28), C14.40(C4⋊D4), (C2×C28).755C23, C4.46(Q8⋊2D7), (C2×D28).16C22, C22.118(C2×D28), C2.15(D56⋊7C2), C2.18(C8.D14), C14.15(C8.C22), C4⋊Dic7.275C22, (C2×Dic14).214C22, (C7×C4⋊C8)⋊8C2, (C2×C56⋊C2).6C2, (C2×C14).138(C2×D4), (C2×C4).700(C22×D7), SmallGroup(448,379)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.36D14
G = < a,b,c,d | a4=b4=1, c14=dbd-1=b-1, d2=b2, ab=ba, cac-1=a-1b2, ad=da, bc=cb, dcd-1=b-1c13 >
Subgroups: 676 in 112 conjugacy classes, 41 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C2×C8, SD16, Q16, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, D4⋊C4, Q8⋊C4, C4⋊C8, C4×Q8, C4.4D4, C2×SD16, C2×Q16, C56, Dic14, Dic14, D28, C2×Dic7, C2×C28, C22×D7, Q8.D4, C56⋊C2, Dic28, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C2×C56, C2×Dic14, C2×D28, C28.44D4, C2.D56, C7×C4⋊C8, C4×Dic14, C4.D28, C2×C56⋊C2, C2×Dic28, C42.36D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C4○D8, C8.C22, D28, C22×D7, Q8.D4, C2×D28, D4×D7, Q8⋊2D7, C4⋊D28, D56⋊7C2, C8.D14, C42.36D14
►On 224 points
Generators in S224
(1 161 199 83)(2 112 200 134)(3 163 201 85)(4 58 202 136)(5 165 203 87)(6 60 204 138)(7 167 205 89)(8 62 206 140)(9 113 207 91)(10 64 208 142)(11 115 209 93)(12 66 210 144)(13 117 211 95)(14 68 212 146)(15 119 213 97)(16 70 214 148)(17 121 215 99)(18 72 216 150)(19 123 217 101)(20 74 218 152)(21 125 219 103)(22 76 220 154)(23 127 221 105)(24 78 222 156)(25 129 223 107)(26 80 224 158)(27 131 169 109)(28 82 170 160)(29 133 171 111)(30 84 172 162)(31 135 173 57)(32 86 174 164)(33 137 175 59)(34 88 176 166)(35 139 177 61)(36 90 178 168)(37 141 179 63)(38 92 180 114)(39 143 181 65)(40 94 182 116)(41 145 183 67)(42 96 184 118)(43 147 185 69)(44 98 186 120)(45 149 187 71)(46 100 188 122)(47 151 189 73)(48 102 190 124)(49 153 191 75)(50 104 192 126)(51 155 193 77)(52 106 194 128)(53 157 195 79)(54 108 196 130)(55 159 197 81)(56 110 198 132)
(1 43 29 15)(2 44 30 16)(3 45 31 17)(4 46 32 18)(5 47 33 19)(6 48 34 20)(7 49 35 21)(8 50 36 22)(9 51 37 23)(10 52 38 24)(11 53 39 25)(12 54 40 26)(13 55 41 27)(14 56 42 28)(57 99 85 71)(58 100 86 72)(59 101 87 73)(60 102 88 74)(61 103 89 75)(62 104 90 76)(63 105 91 77)(64 106 92 78)(65 107 93 79)(66 108 94 80)(67 109 95 81)(68 110 96 82)(69 111 97 83)(70 112 98 84)(113 155 141 127)(114 156 142 128)(115 157 143 129)(116 158 144 130)(117 159 145 131)(118 160 146 132)(119 161 147 133)(120 162 148 134)(121 163 149 135)(122 164 150 136)(123 165 151 137)(124 166 152 138)(125 167 153 139)(126 168 154 140)(169 211 197 183)(170 212 198 184)(171 213 199 185)(172 214 200 186)(173 215 201 187)(174 216 202 188)(175 217 203 189)(176 218 204 190)(177 219 205 191)(178 220 206 192)(179 221 207 193)(180 222 208 194)(181 223 209 195)(182 224 210 196)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224)
(1 42 29 14)(2 13 30 41)(3 40 31 12)(4 11 32 39)(5 38 33 10)(6 9 34 37)(7 36 35 8)(15 28 43 56)(16 55 44 27)(17 26 45 54)(18 53 46 25)(19 24 47 52)(20 51 48 23)(21 22 49 50)(57 144 85 116)(58 115 86 143)(59 142 87 114)(60 113 88 141)(61 140 89 168)(62 167 90 139)(63 138 91 166)(64 165 92 137)(65 136 93 164)(66 163 94 135)(67 134 95 162)(68 161 96 133)(69 132 97 160)(70 159 98 131)(71 130 99 158)(72 157 100 129)(73 128 101 156)(74 155 102 127)(75 126 103 154)(76 153 104 125)(77 124 105 152)(78 151 106 123)(79 122 107 150)(80 149 108 121)(81 120 109 148)(82 147 110 119)(83 118 111 146)(84 145 112 117)(169 214 197 186)(170 185 198 213)(171 212 199 184)(172 183 200 211)(173 210 201 182)(174 181 202 209)(175 208 203 180)(176 179 204 207)(177 206 205 178)(187 196 215 224)(188 223 216 195)(189 194 217 222)(190 221 218 193)(191 192 219 220)
G:=sub<Sym(224)| (1,161,199,83)(2,112,200,134)(3,163,201,85)(4,58,202,136)(5,165,203,87)(6,60,204,138)(7,167,205,89)(8,62,206,140)(9,113,207,91)(10,64,208,142)(11,115,209,93)(12,66,210,144)(13,117,211,95)(14,68,212,146)(15,119,213,97)(16,70,214,148)(17,121,215,99)(18,72,216,150)(19,123,217,101)(20,74,218,152)(21,125,219,103)(22,76,220,154)(23,127,221,105)(24,78,222,156)(25,129,223,107)(26,80,224,158)(27,131,169,109)(28,82,170,160)(29,133,171,111)(30,84,172,162)(31,135,173,57)(32,86,174,164)(33,137,175,59)(34,88,176,166)(35,139,177,61)(36,90,178,168)(37,141,179,63)(38,92,180,114)(39,143,181,65)(40,94,182,116)(41,145,183,67)(42,96,184,118)(43,147,185,69)(44,98,186,120)(45,149,187,71)(46,100,188,122)(47,151,189,73)(48,102,190,124)(49,153,191,75)(50,104,192,126)(51,155,193,77)(52,106,194,128)(53,157,195,79)(54,108,196,130)(55,159,197,81)(56,110,198,132), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,42,29,14)(2,13,30,41)(3,40,31,12)(4,11,32,39)(5,38,33,10)(6,9,34,37)(7,36,35,8)(15,28,43,56)(16,55,44,27)(17,26,45,54)(18,53,46,25)(19,24,47,52)(20,51,48,23)(21,22,49,50)(57,144,85,116)(58,115,86,143)(59,142,87,114)(60,113,88,141)(61,140,89,168)(62,167,90,139)(63,138,91,166)(64,165,92,137)(65,136,93,164)(66,163,94,135)(67,134,95,162)(68,161,96,133)(69,132,97,160)(70,159,98,131)(71,130,99,158)(72,157,100,129)(73,128,101,156)(74,155,102,127)(75,126,103,154)(76,153,104,125)(77,124,105,152)(78,151,106,123)(79,122,107,150)(80,149,108,121)(81,120,109,148)(82,147,110,119)(83,118,111,146)(84,145,112,117)(169,214,197,186)(170,185,198,213)(171,212,199,184)(172,183,200,211)(173,210,201,182)(174,181,202,209)(175,208,203,180)(176,179,204,207)(177,206,205,178)(187,196,215,224)(188,223,216,195)(189,194,217,222)(190,221,218,193)(191,192,219,220)>;
G:=Group( (1,161,199,83)(2,112,200,134)(3,163,201,85)(4,58,202,136)(5,165,203,87)(6,60,204,138)(7,167,205,89)(8,62,206,140)(9,113,207,91)(10,64,208,142)(11,115,209,93)(12,66,210,144)(13,117,211,95)(14,68,212,146)(15,119,213,97)(16,70,214,148)(17,121,215,99)(18,72,216,150)(19,123,217,101)(20,74,218,152)(21,125,219,103)(22,76,220,154)(23,127,221,105)(24,78,222,156)(25,129,223,107)(26,80,224,158)(27,131,169,109)(28,82,170,160)(29,133,171,111)(30,84,172,162)(31,135,173,57)(32,86,174,164)(33,137,175,59)(34,88,176,166)(35,139,177,61)(36,90,178,168)(37,141,179,63)(38,92,180,114)(39,143,181,65)(40,94,182,116)(41,145,183,67)(42,96,184,118)(43,147,185,69)(44,98,186,120)(45,149,187,71)(46,100,188,122)(47,151,189,73)(48,102,190,124)(49,153,191,75)(50,104,192,126)(51,155,193,77)(52,106,194,128)(53,157,195,79)(54,108,196,130)(55,159,197,81)(56,110,198,132), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,42,29,14)(2,13,30,41)(3,40,31,12)(4,11,32,39)(5,38,33,10)(6,9,34,37)(7,36,35,8)(15,28,43,56)(16,55,44,27)(17,26,45,54)(18,53,46,25)(19,24,47,52)(20,51,48,23)(21,22,49,50)(57,144,85,116)(58,115,86,143)(59,142,87,114)(60,113,88,141)(61,140,89,168)(62,167,90,139)(63,138,91,166)(64,165,92,137)(65,136,93,164)(66,163,94,135)(67,134,95,162)(68,161,96,133)(69,132,97,160)(70,159,98,131)(71,130,99,158)(72,157,100,129)(73,128,101,156)(74,155,102,127)(75,126,103,154)(76,153,104,125)(77,124,105,152)(78,151,106,123)(79,122,107,150)(80,149,108,121)(81,120,109,148)(82,147,110,119)(83,118,111,146)(84,145,112,117)(169,214,197,186)(170,185,198,213)(171,212,199,184)(172,183,200,211)(173,210,201,182)(174,181,202,209)(175,208,203,180)(176,179,204,207)(177,206,205,178)(187,196,215,224)(188,223,216,195)(189,194,217,222)(190,221,218,193)(191,192,219,220) );
G=PermutationGroup([[(1,161,199,83),(2,112,200,134),(3,163,201,85),(4,58,202,136),(5,165,203,87),(6,60,204,138),(7,167,205,89),(8,62,206,140),(9,113,207,91),(10,64,208,142),(11,115,209,93),(12,66,210,144),(13,117,211,95),(14,68,212,146),(15,119,213,97),(16,70,214,148),(17,121,215,99),(18,72,216,150),(19,123,217,101),(20,74,218,152),(21,125,219,103),(22,76,220,154),(23,127,221,105),(24,78,222,156),(25,129,223,107),(26,80,224,158),(27,131,169,109),(28,82,170,160),(29,133,171,111),(30,84,172,162),(31,135,173,57),(32,86,174,164),(33,137,175,59),(34,88,176,166),(35,139,177,61),(36,90,178,168),(37,141,179,63),(38,92,180,114),(39,143,181,65),(40,94,182,116),(41,145,183,67),(42,96,184,118),(43,147,185,69),(44,98,186,120),(45,149,187,71),(46,100,188,122),(47,151,189,73),(48,102,190,124),(49,153,191,75),(50,104,192,126),(51,155,193,77),(52,106,194,128),(53,157,195,79),(54,108,196,130),(55,159,197,81),(56,110,198,132)], [(1,43,29,15),(2,44,30,16),(3,45,31,17),(4,46,32,18),(5,47,33,19),(6,48,34,20),(7,49,35,21),(8,50,36,22),(9,51,37,23),(10,52,38,24),(11,53,39,25),(12,54,40,26),(13,55,41,27),(14,56,42,28),(57,99,85,71),(58,100,86,72),(59,101,87,73),(60,102,88,74),(61,103,89,75),(62,104,90,76),(63,105,91,77),(64,106,92,78),(65,107,93,79),(66,108,94,80),(67,109,95,81),(68,110,96,82),(69,111,97,83),(70,112,98,84),(113,155,141,127),(114,156,142,128),(115,157,143,129),(116,158,144,130),(117,159,145,131),(118,160,146,132),(119,161,147,133),(120,162,148,134),(121,163,149,135),(122,164,150,136),(123,165,151,137),(124,166,152,138),(125,167,153,139),(126,168,154,140),(169,211,197,183),(170,212,198,184),(171,213,199,185),(172,214,200,186),(173,215,201,187),(174,216,202,188),(175,217,203,189),(176,218,204,190),(177,219,205,191),(178,220,206,192),(179,221,207,193),(180,222,208,194),(181,223,209,195),(182,224,210,196)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224)], [(1,42,29,14),(2,13,30,41),(3,40,31,12),(4,11,32,39),(5,38,33,10),(6,9,34,37),(7,36,35,8),(15,28,43,56),(16,55,44,27),(17,26,45,54),(18,53,46,25),(19,24,47,52),(20,51,48,23),(21,22,49,50),(57,144,85,116),(58,115,86,143),(59,142,87,114),(60,113,88,141),(61,140,89,168),(62,167,90,139),(63,138,91,166),(64,165,92,137),(65,136,93,164),(66,163,94,135),(67,134,95,162),(68,161,96,133),(69,132,97,160),(70,159,98,131),(71,130,99,158),(72,157,100,129),(73,128,101,156),(74,155,102,127),(75,126,103,154),(76,153,104,125),(77,124,105,152),(78,151,106,123),(79,122,107,150),(80,149,108,121),(81,120,109,148),(82,147,110,119),(83,118,111,146),(84,145,112,117),(169,214,197,186),(170,185,198,213),(171,212,199,184),(172,183,200,211),(173,210,201,182),(174,181,202,209),(175,208,203,180),(176,179,204,207),(177,206,205,178),(187,196,215,224),(188,223,216,195),(189,194,217,222),(190,221,218,193),(191,192,219,220)]])
79 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 56 | 2 | 2 | 2 | 2 | 4 | 28 | 28 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
79 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | C4○D8 | D28 | D56⋊7C2 | C8.C22 | D4×D7 | Q8⋊2D7 | C8.D14 |
| kernel | C42.36D14 | C28.44D4 | C2.D56 | C7×C4⋊C8 | C4×Dic14 | C4.D28 | C2×C56⋊C2 | C2×Dic28 | Dic14 | C2×C28 | C4⋊C8 | C28 | C42 | C2×C8 | C14 | C2×C4 | C2 | C14 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 2 | 3 | 6 | 4 | 12 | 24 | 1 | 3 | 3 | 6 |
Matrix representation of C42.36D14 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 98 | 0 | 0 | 0 |
| 0 | 0 | 0 | 98 | 0 | 0 |
| 0 | 0 | 0 | 0 | 77 | 56 |
| 0 | 0 | 0 | 0 | 108 | 36 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 44 | 0 | 0 |
| 0 | 0 | 81 | 86 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 88 | 88 | 0 | 0 | 0 | 0 |
| 25 | 34 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 7 | 0 | 0 |
| 0 | 0 | 36 | 88 | 0 | 0 |
| 0 | 0 | 0 | 0 | 88 | 64 |
| 0 | 0 | 0 | 0 | 22 | 25 |
| 88 | 88 | 0 | 0 | 0 | 0 |
| 34 | 25 | 0 | 0 | 0 | 0 |
| 0 | 0 | 88 | 106 | 0 | 0 |
| 0 | 0 | 41 | 25 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 49 |
| 0 | 0 | 0 | 0 | 38 | 88 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,98,0,0,0,0,0,0,98,0,0,0,0,0,0,77,108,0,0,0,0,56,36],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,27,81,0,0,0,0,44,86,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[88,25,0,0,0,0,88,34,0,0,0,0,0,0,112,36,0,0,0,0,7,88,0,0,0,0,0,0,88,22,0,0,0,0,64,25],[88,34,0,0,0,0,88,25,0,0,0,0,0,0,88,41,0,0,0,0,106,25,0,0,0,0,0,0,25,38,0,0,0,0,49,88] >;
C42.36D14 in GAP, Magma, Sage, TeX
C_4^2._{36}D_{14} % in TeX
G:=Group("C4^2.36D14"); // GroupNames label
G:=SmallGroup(448,379);
// by ID
G=gap.SmallGroup(448,379);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,254,219,58,1123,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d*b*d^-1=b^-1,d^2=b^2,a*b=b*a,c*a*c^-1=a^-1*b^2,a*d=d*a,b*c=c*b,d*c*d^-1=b^-1*c^13>;
// generators/relations